An Analytic Solution for Asset Allocation with a Multivariate Laplace Distribution

TL;DR

This paper derives an analytical solution for asset allocation assuming returns follow a multivariate Laplace distribution, extending previous elliptically symmetric models and addressing specific distributional nuances.

Contribution

It specializes existing elliptically symmetric distribution models to the multivariate Laplace case, providing a more accurate analytical asset allocation solution.

Findings

The solution aligns closely with previous conjectures but includes additional terms.

Rescaling of variance accounts for different parameterizations of the Laplace distribution.

The approach enhances understanding of asset allocation under Laplace-distributed returns.

Abstract

In this short note the theory for multivariate asset allocation with elliptically symmetric distributions of returns, as developed in the author's prior work, is specialized to the case of returns drawn from a multivariate Laplace distribution. This analysis delivers a result closely, but not perfectly, consistent with the conjecture presented in the author's article Thinking Differently About Asset Allocation. The principal differences are due to the introduction of a term in the dimensionality of the problem, which was omitted from the conjectured solution, and a rescaling of the variance due to varying parameterizations of the univariate Laplace distribution.